## Not So Easy

Just before the turn of the Century, Steven Hawking had to admit that, what he had ventured to predict twenty years earlier, that the Legacy System of Physical Theory (LST) was on the verge of being able to explain all things physical, was a little premature. Now, more than ten years after that, he has suggested that the LST community has no choice but to give up altogether, in its quest for a unified physical theory.

Our argument has always been that the LST cannot get there from here, but we don’t need M theory to prove that. The LST theory of the electron will suffice. It is necessarily defined as a point particle, but since it must also carry a charge and quantum spin, this introduces an insurmountable contradiction, due to the impossibility of dividing anything by zero and defining the spin of nothing. Nevertheless, the LST has simply overlooked these impossible contradictions, until, after many generations and trillions of dollars have been spent, it has to admit utter failure.

Certainly, the new Reciprocal System of Physical Theory (RST) does not have all the answers either, but the fact that it is a new system of theory, the first since Newton’s, is universally welcome news. Indeed, the RST has come a long way towards producing a unified theory, considering the scant resources available to its researchers. Moreover, its simplicity is profoundly appealing, given the complexities and problems of the LST.

It’s important to note that, just as we can consider the LST to be a program of research built on Newton’s second law of motion, we can regard the RST to be a program of research based on the implications of Newton’s third law of motion, which is to say that there are two and only two “directions” in a given dimension, and, since only three dimensions have ever been observed in any given physical system, then it follows that all physical magnitudes must be derived from these three, dual, dimensions.

The genius of the RST is that it starts, not with the motion of pre-existent objects in a 3D frame of reference, as does the LST, but rather it begins with the progression of two reciprocal quantities that are as observable as are objects, but these quantities have no need for an external frame of reference to define them. Everything in the system comes from the relationship of these two quantities - and nothing else.

Of all the great philosophical strengths such a system offers, none is greater than this: The theories of the RST are deduced from its fundamental postulates, which conform to the “directional” and dimensional properties of numbers. Since all of the system’s physical magnitudes are generated by the fact that there are two “directions” in each of three dimensions, in each of its two, reciprocal, quantities, space and time, it corresponds perfectly to the possible combinations of the multi-dimensional numbers found in the tetraktys.

This leads to two reciprocal sectors in the mathematical/physical universe. In the first sector, we can write the set of multi-dimensional numbers in the tetraktys as,

s/t = 20/20, 21/20, 22/20, 23/20,

corresponding to the spatial geometry characterized by the two potential “directions” in the zero dimensions of a point, the two actual “directions” in the one dimension of a line, the four in the two dimensions of an area and the eight in the three dimensions of a volume.

The reciprocal of these multi-dimensional numbers constitutes the set of multi-dimensional numbers of the reciprocal tetraktys of the second sector,

s/t = 20/20, 20/21, 20/22, 20/23,

corresponding to the temporal “geometry” characterized by the two potential “directions” in the zero dimensions of a point, the two actual “directions” in the one dimension of a line, the four in the two dimensions of an area and the eight in the three dimensions of a volume.

Of course, this is a fundamental and radical departure from the foundation of the LST, based on what we may be so bold to call the legacy system of mathematics (LSM). The LSM does not explicitly employ the principle of reciprocity inherent in the relationship of space and time, but instead substitutes the *ad hoc *invention of the square root of -1, together with the concept of rotation, to define the multi-dimensional numbers of the tetraktys.

This makes it necessary to define a reciprocal system of mathematics (RSM), based on the dual tetraktys just described. The RSM limits us to the three dimensions of the dual tetraktys, but it frees us from the dead-end trap of complex, quaternion and octonion numbers, based on *ad hoc *inventions of imaginary numbers. This is the dead-end that has led the LST community to its present impasse.

Since the scientist that now sits in Newton’s Chair admits that the great program of research initiated by Newton has irreconcilably lost its way in the labyrinth of “extra” dimensions, it’s time to look to a new program of research, one that lives within the observable limits of nature.

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